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A081568
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Third binomial transform of F(n+1).
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4
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1, 4, 17, 75, 338, 1541, 7069, 32532, 149965, 691903, 3193706, 14745009, 68084297, 314394980, 1451837593, 6704518371, 30961415074, 142980203437, 660285858245, 3049218769908, 14081386948661, 65028302171639, 300302858766202
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A081567. Case k=3 of family of recurrences a(n)=(2k+1)a(n-1)-A028387(k-1)a(n-2), a(0)=1,a(1)=k+1.
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FORMULA
| a(n)=7a(n-1)-11a(n-2), a(0)=1, a(1)=4. a(n)=(1/2 - sqrt(5)/10)(7/2 - sqrt(5)/2)^n + (sqrt(5)/10 + 1/2)(sqrt(5)/2 + 7/2)^n G.f.: (1-3x)/(1-7x+11x^2).
a(n)= Sum_{k, 0<=k<=n} A094441(n,k)*3^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 14 2009]
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CROSSREFS
| Cf. A000045.
Sequence in context: A086351 A049027 A026751 * A026378 A151247 A117439
Adjacent sequences: A081565 A081566 A081567 * A081569 A081570 A081571
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 22 2003
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